The number n = Product_j p_j can be regarded as an index for the multiset of all the j's, occurring with multiplicity corresponding to the highest power of p_j dividing n. Then a(n) is the gcd of the elements of this multiset. Compare A056239, where the same encoding for integer multisets('Heinz encoding') is used, but where A056239(n) is the sum, rather than the gcd, of the elements of the corresponding multiset (partition) of the j's. Cf. also A003963, for which A003963(n) is the product of the elements of the corresponding multiset.